A universal flow invariant in quantum field theory
Abstract
A flow invariant is a quantity depending only on the ultraviolet (UV) and infrared (IR) conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically conformal field theories, scale invariance is broken by quantum effects and the flow invariant a_{UV}a_{IR} is measured by the area of the graph of the beta function between the fixed points. There exists a theoretical explanation of this nontrivial fact. On the other hand, when scale invariance is broken at the classical level, it is known empirically that the flow invariant equals c_{UV}c_{IR} in massive freefield theories, but a theoretical argument explaining why it is so is still missing. A number of related open questions are answered here. A general formula of the flow invariant is found, which also holds when the stress tensor has improvement terms. The conditions under which the flow invariant equals c_{UV}c_{IR} are identified. Several nonunitary theories are used as a laboratory, but the conclusions are general and an application to the Standard Model is addressed. The analysis of the results suggests some new minimum principles, which might point towards a new understanding of quantum field theory.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 November 2001
 DOI:
 10.1088/02649381/18/21/304
 arXiv:
 arXiv:hepth/0101088
 Bibcode:
 2001CQGra..18.4417A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 28 pages, 3 figures